Gloria would like to construct a box with volume of exactly 35ft^3 using only metal and wood. The metal costs $15/ft^2 and the wood costs $9/ft^2. If the wood is to go on the sides, the metal is to go on the top and bottom, and if the length of the base is to be 3 times the width of the base, find the dimensions of the box that will minimize the cost of construction. Round your answer to the nearest four decimal places.
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